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On the nature of diffuse satellites in the electron diffraction patterns of lead orthovanadate and lead orthophosphate
Solid State Communications, Printed in Great Britain.
Vol. 60, No. 9, pp. 749-75
ON THE NATURE OF DIFFUSE SATELLITES ORTHOVANADATE C. Manolikas*, University
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
1, 1986.
IN THE ELECTRON DIFFRACTION AND LEAD ORTHOPHOSPHATE
PATTERNS
OF LEAD
G. Van Tendeloo and S. Arnelinckxt
of Antwerp (RUCA), Groenenborgerlaan
171 2020Antwerpen,
Belgium
(Received 20 June 1986 by E. Burstein) It is shown that the static or dynamic nature of diffuse scattering in electron diffraction patterns can be determined by comparing the electron diffraction pattern with the optical diffraction pattern of a high resolution image made under the same illumination conditions. The method is applied to show that the diffuse satellites observed in lead orthovanadate are due to a softening boundary mode.
1. INTRODUCTION IN A RECENT PAPER [l] we pointed out that high resolution electron microscopy combined with optical diffraction, using the high resolution images as gratings provides a simple method to differentiate between the static or the dynamic origin of diffuse scattering in electron diffraction patterns. The method is based on the fact that the interaction time of the electrons with the specimen is extremely short. The recorded electron diffraction pattern is thus the superposition of instantaneous diffraction patterns produced by a rapid succession of slightly different geometrical situations. On the other hand the lattice of images of atom columns is a time average of their instantaneous positions. These average positions are not changed by harmonic oscillations. Although the anharmonicity of the vibrations might change somewhat the interatomic distances, as a result of thermal expansion this does not affect the perfection of the lattice. The period of atom vibrations being very much longer than the exposure time of a high resolution electron photograph, the micrograph inevitably records the time average of the atom positions. If the optical diffracton pattern reveals the same diffuse scattering as the electron diffraction pattern the origin is static disorder. If on the contrary the optical diffraction pattern does not reveal the diffuse scattering, but does reveal the Bragg spots clearly, the average lattice is still perfect and the diffuse scattering has a dynamic origin. The validity of the method was illustrated by means of three examples, in the field of alloys; two static and one dynamic phenomenon were studied [l] .
* Permanent address: University of Thessaloniki, Greece. t Also at: S.C.K., 2400-MOL, Belgium.
Thessaloniki,
749
We have now applied this method to the problem of the origin of diffuse satellites in the diffraction patterns of lead orthophosphate and lead orthovanadate. The value of the method has hereby been confirmed on a quite different system. The observations have moreover made it possible to construct a coherent picture of the phase transitions in these materials. 2. DIFFRACTION
EFFECTS
We have recently shown that diffuse spots occur in the diffraction pattern of lead orthovanadate as well as in lead orthophosphate [2,3]. In lead orthovanadate it was found that the stars of six satellites associated with each Bragg spot, which appear already at temperatures above the ~-+3 transition temperature, sharpen up on cooling in a temperature range from 317-377 K. It was shown that they reveal a metastable rhombohedral superstructure called y’, with lattice parameters which are twice as large as those of the rhombohedral T-phase and which occurs in certain crystal parts only. The y’regions do not exhibit orientation variants since there is no reduction in rotation symmetry on going from y + 7’. In rhombohedral Plead orthophosphate similar sixfold configurations of diffuse satellite spots occur around each Bragg spot at temperatures slightly above the transition temperature /I + 0~. Like in lead orthovanadate the spots also become sharp on lowering the temperature, without changing their positions. Dark field images made in different sharp spots now reveal three orientation variants of the low temperature (Yphase. This behaviour is strikingly different from that of the vanadate. The dynamic origin of the spots in the Pphase of the orthophosphate was demonstrated previously be means of neutron diffraction [4-61 and Raman scattering [6-81. The diffuse spots were attributed to the
750
LEAD ORTHOVANADATE
AND LEAD ORTHOPHOSPHATE
Fig. 1. (a) Bright field high resolution image of lead orthovanadate along the zone normal to the cleavage plane (the [0 00 I] ,, zone) obtained by collecting one ring of Bragg spots with their satellites (see b): (b) Diffraction pattern along the same zone. The selected part of the diffraction pattern includes the first hexagon of Bragg spots. The shadow of the aperture which is visible on the photograph refers to the satellite dark field image which is mentioned in the text. (c) Optical diffraction pattern of the high resolution image (a). Note the presence of well defined Bragg spots, with the correct relative intensities. Note also the absence of any indication of satellite spots. softening of a threefold degenerated zone boundary mode. AS yet similar experiments were not performed on the orthovanadate, but we suggested that also in this case the diffuse spots might be dynamic in nature [2, 31. 3. DIFFUSE
SCATTERING
It is the purpose of this note to show that this can be demonstrated using the simple method outlined in
[Il. Above about 100°C specimens of lead orthovanadate produce a diffraction pattern such as shown in Fig. 1 (b) which prominently exhibits six diffuse satellites around each Bragg spot due to the basic structure. A high resolution image, made by selecting the first hexagon of Bragg spots, as well as the associated satellites
Vol. 60, No. 9
is reproduced in Fig. l(a) where also the unit cell of the projected structure is indicated. The optical diffraction pattern made by using such a high resolution image as a diffraction grating and a laser beam as a light source is reproduced in Fig. l(c); it shows no trace of the diffuse satellites but reproduces quite well the geometry and even the relative intensities of the first hexagon of Bragg spots. This proves that the static or averaged information in the diffraction pattern has been adequately recorded in the image. The absence of any trace of satellites in the optical diffraction pattern proves that these spots have a dynamic origin. Also the high resolution image (a) does not show any superperiod modulation of the dot pattern as one would expect when making the image corresponding with a diffraction pattern exhibiting satellites of such large intensity. This observation thus confirms in a simple way that like in the phosphate the satellites are due to a softening mode. In dark field images made in the clusters of six satellites associated with a single Bragg reflection no fragmentation in domains is observed, which is consistent with their dynamic nature. One complication associated with the application of this method might arise from the successive use of the microscope in two different modes. When switching from the diffraction mode to the high resolution imaging mode it is usually required to increase somewhat the local beam intensity, which may lead to an increase in the specimen temperature thereby losing the diffuse satellites. We avoided this problem by convincing ourselves, after having made the high resolution image and without changing the illumination conditions, that the diffraction pattern still exhibited the satellites. Ahernatively, we also made first the focused diffraction pattern formed under illumination conditions appropriate for high resolution, and subsequently made the image, without changing the illumination conditions. 4. DISCUSSION The behaviour at the y + y’ transition in the vanadate and at the 0 + (Ytransition in the phosphate can now be understood. In both materials gradual softening of the same type of zone boundary mode already occurs in the high temperature phase just above the transition temperature. In both materials this mode is triply degenerate. On cooling through the transition point the degeneracy is removed at the y + fl transition in the vanadate and at the /~-+cx transition in the phosphate. However in the vanadate apparently the soft mode may freeze-in either as a single 3-q-state and form the metastable y’-phase, or as three separate l-q states thus forming the monoclinic /3 phase, fragmented in three monoclinic orientation variants.
Vol. 60, No. 9
LEAD ORTHOVANADATE
7.51
AND LEAD ORTHOPHOSPHATE
In the phosphate an intermediate phase, which would be the homologue of the y’-phase, has not been observed as yet; it is possible that such a phase does not exist and that only l-q states are formed at once. 5. CONCLUSION High resolution electron microscopy provides a simple method to prove the dynamical character of the diffuse satellites in the lead orthovanadate. The satellites reveal a triply degenerate soft zone boundary mode. This mode can either freeze-in as a single 3q-state or as three lq-state. In the latter case the crystal is fragmented in domains containing each one of three different monoclinic orientation states.
In the formed.
former
case
the
rhombohedral
y’-phase
is
REFERENCES 1. *. 3. 4. 5. 6.
G. Van Tendeloo & S. Amelinckx, Scripta Met. 20, 335 (1986). C. Manolikas, E. Paloura, G. Van Tendeloo & S. Amelinckx, Mat. Res. Bull. (1986) to be published. C. Manolikas, G. Van Tendeloo & S. Amelinckx, Mat. Res. Bull (1986) to be published. J.P. Benoit, B. Hennion & M. Lambert, Phase Trans. 2, 102 (1981). C. Joffrin, J.P. Benoit, R. Currat & M. Lambert, .I. Physique 40, 1185 (1979). V. Bismayer, E. Salje & C. Joffrin, J. Physique 43, 1379 (1982). J.P. Benoit, Ferroelectrics 13,331 (1976). E. Salje & U. Bismayer, Phase Trans. 2, 15 (1981).
Vol. 60, No. 9, pp. 749-75
ON THE NATURE OF DIFFUSE SATELLITES ORTHOVANADATE C. Manolikas*, University
0038-1098/86 $3.00 + .OO Pergamon Journals Ltd.
1, 1986.
IN THE ELECTRON DIFFRACTION AND LEAD ORTHOPHOSPHATE
PATTERNS
OF LEAD
G. Van Tendeloo and S. Arnelinckxt
of Antwerp (RUCA), Groenenborgerlaan
171 2020Antwerpen,
Belgium
(Received 20 June 1986 by E. Burstein) It is shown that the static or dynamic nature of diffuse scattering in electron diffraction patterns can be determined by comparing the electron diffraction pattern with the optical diffraction pattern of a high resolution image made under the same illumination conditions. The method is applied to show that the diffuse satellites observed in lead orthovanadate are due to a softening boundary mode.
1. INTRODUCTION IN A RECENT PAPER [l] we pointed out that high resolution electron microscopy combined with optical diffraction, using the high resolution images as gratings provides a simple method to differentiate between the static or the dynamic origin of diffuse scattering in electron diffraction patterns. The method is based on the fact that the interaction time of the electrons with the specimen is extremely short. The recorded electron diffraction pattern is thus the superposition of instantaneous diffraction patterns produced by a rapid succession of slightly different geometrical situations. On the other hand the lattice of images of atom columns is a time average of their instantaneous positions. These average positions are not changed by harmonic oscillations. Although the anharmonicity of the vibrations might change somewhat the interatomic distances, as a result of thermal expansion this does not affect the perfection of the lattice. The period of atom vibrations being very much longer than the exposure time of a high resolution electron photograph, the micrograph inevitably records the time average of the atom positions. If the optical diffracton pattern reveals the same diffuse scattering as the electron diffraction pattern the origin is static disorder. If on the contrary the optical diffraction pattern does not reveal the diffuse scattering, but does reveal the Bragg spots clearly, the average lattice is still perfect and the diffuse scattering has a dynamic origin. The validity of the method was illustrated by means of three examples, in the field of alloys; two static and one dynamic phenomenon were studied [l] .
* Permanent address: University of Thessaloniki, Greece. t Also at: S.C.K., 2400-MOL, Belgium.
Thessaloniki,
749
We have now applied this method to the problem of the origin of diffuse satellites in the diffraction patterns of lead orthophosphate and lead orthovanadate. The value of the method has hereby been confirmed on a quite different system. The observations have moreover made it possible to construct a coherent picture of the phase transitions in these materials. 2. DIFFRACTION
EFFECTS
We have recently shown that diffuse spots occur in the diffraction pattern of lead orthovanadate as well as in lead orthophosphate [2,3]. In lead orthovanadate it was found that the stars of six satellites associated with each Bragg spot, which appear already at temperatures above the ~-+3 transition temperature, sharpen up on cooling in a temperature range from 317-377 K. It was shown that they reveal a metastable rhombohedral superstructure called y’, with lattice parameters which are twice as large as those of the rhombohedral T-phase and which occurs in certain crystal parts only. The y’regions do not exhibit orientation variants since there is no reduction in rotation symmetry on going from y + 7’. In rhombohedral Plead orthophosphate similar sixfold configurations of diffuse satellite spots occur around each Bragg spot at temperatures slightly above the transition temperature /I + 0~. Like in lead orthovanadate the spots also become sharp on lowering the temperature, without changing their positions. Dark field images made in different sharp spots now reveal three orientation variants of the low temperature (Yphase. This behaviour is strikingly different from that of the vanadate. The dynamic origin of the spots in the Pphase of the orthophosphate was demonstrated previously be means of neutron diffraction [4-61 and Raman scattering [6-81. The diffuse spots were attributed to the
750
LEAD ORTHOVANADATE
AND LEAD ORTHOPHOSPHATE
Fig. 1. (a) Bright field high resolution image of lead orthovanadate along the zone normal to the cleavage plane (the [0 00 I] ,, zone) obtained by collecting one ring of Bragg spots with their satellites (see b): (b) Diffraction pattern along the same zone. The selected part of the diffraction pattern includes the first hexagon of Bragg spots. The shadow of the aperture which is visible on the photograph refers to the satellite dark field image which is mentioned in the text. (c) Optical diffraction pattern of the high resolution image (a). Note the presence of well defined Bragg spots, with the correct relative intensities. Note also the absence of any indication of satellite spots. softening of a threefold degenerated zone boundary mode. AS yet similar experiments were not performed on the orthovanadate, but we suggested that also in this case the diffuse spots might be dynamic in nature [2, 31. 3. DIFFUSE
SCATTERING
It is the purpose of this note to show that this can be demonstrated using the simple method outlined in
[Il. Above about 100°C specimens of lead orthovanadate produce a diffraction pattern such as shown in Fig. 1 (b) which prominently exhibits six diffuse satellites around each Bragg spot due to the basic structure. A high resolution image, made by selecting the first hexagon of Bragg spots, as well as the associated satellites
Vol. 60, No. 9
is reproduced in Fig. l(a) where also the unit cell of the projected structure is indicated. The optical diffraction pattern made by using such a high resolution image as a diffraction grating and a laser beam as a light source is reproduced in Fig. l(c); it shows no trace of the diffuse satellites but reproduces quite well the geometry and even the relative intensities of the first hexagon of Bragg spots. This proves that the static or averaged information in the diffraction pattern has been adequately recorded in the image. The absence of any trace of satellites in the optical diffraction pattern proves that these spots have a dynamic origin. Also the high resolution image (a) does not show any superperiod modulation of the dot pattern as one would expect when making the image corresponding with a diffraction pattern exhibiting satellites of such large intensity. This observation thus confirms in a simple way that like in the phosphate the satellites are due to a softening mode. In dark field images made in the clusters of six satellites associated with a single Bragg reflection no fragmentation in domains is observed, which is consistent with their dynamic nature. One complication associated with the application of this method might arise from the successive use of the microscope in two different modes. When switching from the diffraction mode to the high resolution imaging mode it is usually required to increase somewhat the local beam intensity, which may lead to an increase in the specimen temperature thereby losing the diffuse satellites. We avoided this problem by convincing ourselves, after having made the high resolution image and without changing the illumination conditions, that the diffraction pattern still exhibited the satellites. Ahernatively, we also made first the focused diffraction pattern formed under illumination conditions appropriate for high resolution, and subsequently made the image, without changing the illumination conditions. 4. DISCUSSION The behaviour at the y + y’ transition in the vanadate and at the 0 + (Ytransition in the phosphate can now be understood. In both materials gradual softening of the same type of zone boundary mode already occurs in the high temperature phase just above the transition temperature. In both materials this mode is triply degenerate. On cooling through the transition point the degeneracy is removed at the y + fl transition in the vanadate and at the /~-+cx transition in the phosphate. However in the vanadate apparently the soft mode may freeze-in either as a single 3-q-state and form the metastable y’-phase, or as three separate l-q states thus forming the monoclinic /3 phase, fragmented in three monoclinic orientation variants.
Vol. 60, No. 9
LEAD ORTHOVANADATE
7.51
AND LEAD ORTHOPHOSPHATE
In the phosphate an intermediate phase, which would be the homologue of the y’-phase, has not been observed as yet; it is possible that such a phase does not exist and that only l-q states are formed at once. 5. CONCLUSION High resolution electron microscopy provides a simple method to prove the dynamical character of the diffuse satellites in the lead orthovanadate. The satellites reveal a triply degenerate soft zone boundary mode. This mode can either freeze-in as a single 3q-state or as three lq-state. In the latter case the crystal is fragmented in domains containing each one of three different monoclinic orientation states.
In the formed.
former
case
the
rhombohedral
y’-phase
is
REFERENCES 1. *. 3. 4. 5. 6.
G. Van Tendeloo & S. Amelinckx, Scripta Met. 20, 335 (1986). C. Manolikas, E. Paloura, G. Van Tendeloo & S. Amelinckx, Mat. Res. Bull. (1986) to be published. C. Manolikas, G. Van Tendeloo & S. Amelinckx, Mat. Res. Bull (1986) to be published. J.P. Benoit, B. Hennion & M. Lambert, Phase Trans. 2, 102 (1981). C. Joffrin, J.P. Benoit, R. Currat & M. Lambert, .I. Physique 40, 1185 (1979). V. Bismayer, E. Salje & C. Joffrin, J. Physique 43, 1379 (1982). J.P. Benoit, Ferroelectrics 13,331 (1976). E. Salje & U. Bismayer, Phase Trans. 2, 15 (1981).